So I have a 24-Bit/48khz DTS-HD file that imported into Audacity with my project settings at 48khz/32-bit Float and highest quality/no dithering. I trimmed and faded in/out the various channels within the file. I then saved a lossless version of the project that created WAV's for each channel. I plan on downmixing the file into a 24-bit flac.
My questions: Have I messed up the audio quality of the final output switching between 24-bit and 32-bit float? Should I change the settings to 24-bit or just output the file to a 32-bit float file? Should I dither at all during my editing process?
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Dither may be necessary anytime you go from a higher bit depth to a lower.
So, 32bit (float or integer) -> 24bit : yes.
The reverse is not true.
Note, if you are doing simple edits, staying in same bitdepth doesn't/shouldn't require dither, however if you use DSP (fades, mixes, eq, comp. gain, fx), those dsp algorithms OFTEN require math operations in much higher bitdepth (e.g. 48bit, 64bit...) before returning the result which is again the starting bitdepth. This dsp change back ALSO should incorporate dither, though very often it doesn't.
Note also, that the difference between using dither and not using it becomes more apparent the lower your resulting bitdepth. So 64 -> 32 without dither isn't a major loss, but 32 -> 16 may be, and 16 -> 8 very much is.
These rules also hold true when dealing with graphics (still or video).
32 bit float (24 bit significant + 8 bit mantissa) provide same accuracy as 24 bit integer thus no need for dither (possible 1:1 mapping). From practical perspective dither (better combined with noise-shaping) is recommended at the last step before reproduction (feeding PCM samples to DAC).
Dithering for intermediate products is not recommended (dither will be accumulated and overall SNR worse - noise floor artificially elevated).
It is wise to perform all processing within same number representation (sufficient integer - 24 bit is OK when careful signal processing is performed or float when higher dynamic than absolute accuracy is required).
Intermediate "Not recommended" as a theoretical ideal, as repetitively "adding noise" doesn't sound like a good idea in general. But if you are talking about LSB - 1/3 LSB noise, at 24bit or greater bitdepths, IN PRACTICE, you could do it multiple multiples of times and only be adding say 20dB of noise to your theoretical -144dB noise floor, giving you a new noise floor of -124dB. So, STILL very, very good. And if you use higher bitdepths, it would be better still (hence my recommendation of using it in interim processes).
Otherwise, I agree with the majority of what you said.